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The Functional Calculus For Sectorial Operators
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Book Synopsis The Functional Calculus for Sectorial Operators by : Markus Haase
Download or read book The Functional Calculus for Sectorial Operators written by Markus Haase and published by Springer Science & Business Media. This book was released on 2006-08-18 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a systematic and partly axiomatic treatment of the holomorphic functional calculus for unbounded sectorial operators. The account is generic so that it can be used to construct and interrelate holomorphic functional calculi for other types of unbounded operators. Particularly, an elegant unified approach to holomorphic semigroups is obtained. The last chapter describes applications to PDE, evolution equations and approximation theory as well as the connection with harmonic analysis.
Book Synopsis Analysis in Banach Spaces by : Tuomas Hytönen
Download or read book Analysis in Banach Spaces written by Tuomas Hytönen and published by Springer. This book was released on 2018-02-14 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory. It presents a thorough study of the fundamental randomisation techniques and the operator-theoretic aspects of the theory. The first two chapters address the relevant classical background from the theory of Banach spaces, including notions like type, cotype, K-convexity and contraction principles. In turn, the next two chapters provide a detailed treatment of the theory of R-boundedness and Banach space valued square functions developed over the last 20 years. In the last chapter, this content is applied to develop the holomorphic functional calculus of sectorial and bi-sectorial operators in Banach spaces. Given its breadth of coverage, this book will be an invaluable reference to graduate students and researchers interested in functional analysis, harmonic analysis, spectral theory, stochastic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations.
Book Synopsis Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes by : Fabrizio Colombo
Download or read book Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes written by Fabrizio Colombo and published by Springer. This book was released on 2019-07-10 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a new theory for evolution operators and a new method for defining fractional powers of vector operators. This new approach allows to define new classes of fractional diffusion and evolution problems. These innovative methods and techniques, based on the concept of S-spectrum, can inspire researchers from various areas of operator theory and PDEs to explore new research directions in their fields. This monograph is the natural continuation of the book: Spectral Theory on the S-Spectrum for Quaternionic Operators by Fabrizio Colombo, Jonathan Gantner, and David P. Kimsey (Operator Theory: Advances and Applications, Vol. 270).
Book Synopsis Functional Calculus for Bisectorial Operators and Applications to Linear and Non-linear Evolution Equations by : Markus Duelli
Download or read book Functional Calculus for Bisectorial Operators and Applications to Linear and Non-linear Evolution Equations written by Markus Duelli and published by . This book was released on 2005 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The holomorphic functional calculus for sectorial unbounded operators is an extension of the classical Dunford calculus for bounded operators. The interest in this calculus is motivated by the Kato square root problem and applications to the operator-sum method introduced by DaPrato and Grisvard to treat evolution equations on a finite interval. In this thesis we develop the holomorphic functional calculus for multisectorial and asymptotically bisectorial operators. We obtain versions of closed-sum theorems that allow to deduce maximal regularity for first and second order Cauchy problems both on the line and for the periodic problem. The results are then applied to prove existence and uniqueness of non-linear evolution equations.
Book Synopsis Partial Differential Equations and Functional Analysis by : Erik Koelink
Download or read book Partial Differential Equations and Functional Analysis written by Erik Koelink and published by Springer Science & Business Media. This book was released on 2006-08-18 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Capturing the state of the art of the interplay between partial differential equations, functional analysis, maximal regularity, and probability theory, this volume was initiated at the Delft conference on the occasion of the retirement of Philippe Clément. It will be of interest to researchers in PDEs and functional analysis.
Book Synopsis Riesz Transforms, Hodge-Dirac Operators and Functional Calculus for Multipliers by : Cédric Arhancet
Download or read book Riesz Transforms, Hodge-Dirac Operators and Functional Calculus for Multipliers written by Cédric Arhancet and published by Springer Nature. This book was released on 2022-05-05 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on recent research in noncommutative harmonic analysis treats the Lp boundedness of Riesz transforms associated with Markovian semigroups of either Fourier multipliers on non-abelian groups or Schur multipliers. The detailed study of these objects is then continued with a proof of the boundedness of the holomorphic functional calculus for Hodge–Dirac operators, thereby answering a question of Junge, Mei and Parcet, and presenting a new functional analytic approach which makes it possible to further explore the connection with noncommutative geometry. These Lp operations are then shown to yield new examples of quantum compact metric spaces and spectral triples. The theory described in this book has at its foundation one of the great discoveries in analysis of the twentieth century: the continuity of the Hilbert and Riesz transforms on Lp. In the works of Lust-Piquard (1998) and Junge, Mei and Parcet (2018), it became apparent that these Lp operations can be formulated on Lp spaces associated with groups. Continuing these lines of research, the book provides a self-contained introduction to the requisite noncommutative background. Covering an active and exciting topic which has numerous connections with recent developments in noncommutative harmonic analysis, the book will be of interest both to experts in no-commutative Lp spaces and analysts interested in the construction of Riesz transforms and Hodge–Dirac operators.
Book Synopsis Functional Analytic Methods for Evolution Equations by : Giuseppe Da Prato
Download or read book Functional Analytic Methods for Evolution Equations written by Giuseppe Da Prato and published by Springer. This book was released on 2004-08-30 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations. In particular the contributions deal with Markov semigroups, maximal L^p-regularity, optimal control problems for boundary and point control systems, parabolic moving boundary problems and parabolic nonautonomous evolution equations. The book is addressed to PhD students, young researchers and mathematicians doing research in one of the above topics.
Book Synopsis Operators, Semigroups, Algebras and Function Theory by : Yemon Choi
Download or read book Operators, Semigroups, Algebras and Function Theory written by Yemon Choi and published by Springer Nature. This book was released on 2023-12-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects contributions from participants in the IWOTA conference held virtually at Lancaster, UK, originally scheduled in 2020 but postponed to August 2021. It includes both survey articles and original research papers covering some of the main themes of the meeting.
Book Synopsis Recent Advances in Operator Theory and Applications by : Tsuyoshi Ando
Download or read book Recent Advances in Operator Theory and Applications written by Tsuyoshi Ando and published by Springer Science & Business Media. This book was released on 2008-12-19 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the International Workshop on Operator Theory and Applications (IWOTA 2006) held at Seoul National University, Seoul, Korea, from July 31 to August 3, 2006. This volume contains sixteen research papers which reflect developments in operator theory and applications.
Book Synopsis Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics by : Wolfgang Arendt
Download or read book Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics written by Wolfgang Arendt and published by Birkhäuser. This book was released on 2015-12-10 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume originates from a conference held in Herrnhut in June 2013. It provides unique insights into the power of abstract methods and techniques in dealing successfully with numerous applications stemming from classical analysis and mathematical physics. The book features diverse topics in the area of operator semigroups, including partial differential equations, martingale and Hilbert transforms, Banach and von Neumann algebras, Schrödinger operators, maximal regularity and Fourier multipliers, interpolation, operator-theoretical problems (concerning generation, perturbation and dilation, for example), and various qualitative and quantitative Tauberian theorems with a focus on transfinite induction and magics of Cantor. The last fifteen years have seen the dawn of a new era for semigroup theory with the emphasis on applications of abstract results, often unexpected and far removed from traditional ones. The aim of the conference was to bring together prominent experts in the field of modern semigroup theory, harmonic analysis, complex analysis and mathematical physics, and to present the lively interactions between all of those areas and beyond. In addition, the meeting honored the sixtieth anniversary of Prof C. J. K. Batty, whose scientific achievements are an impressive illustration of the conference goal. These proceedings present contributions by prominent scientists at this international conference, which became a landmark event. They will be a valuable and inspiring source of information for graduate students and established researchers.
Book Synopsis Operator Theory on One-Sided Quaternion Linear Spaces: Intrinsic $S$-Functional Calculus and Spectral Operators by : Jonathan Gantner
Download or read book Operator Theory on One-Sided Quaternion Linear Spaces: Intrinsic $S$-Functional Calculus and Spectral Operators written by Jonathan Gantner and published by American Mathematical Society. This book was released on 2021-02-10 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two major themes drive this article: identifying the minimal structure necessary to formulate quaternionic operator theory and revealing a deep relation between complex and quaternionic operator theory. The theory for quaternionic right linear operators is usually formulated under the assumption that there exists not only a right- but also a left-multiplication on the considered Banach space $V$. This has technical reasons, as the space of bounded operators on $V$ is otherwise not a quaternionic linear space. A right linear operator is however only associated with the right multiplication on the space and in certain settings, for instance on quaternionic Hilbert spaces, the left multiplication is not defined a priori, but must be chosen randomly. Spectral properties of an operator should hence be independent of the left multiplication on the space.
Book Synopsis Quantized Number Theory, Fractal Strings And The Riemann Hypothesis: From Spectral Operators To Phase Transitions And Universality by : Hafedh Herichi
Download or read book Quantized Number Theory, Fractal Strings And The Riemann Hypothesis: From Spectral Operators To Phase Transitions And Universality written by Hafedh Herichi and published by World Scientific. This book was released on 2021-07-27 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studying the relationship between the geometry, arithmetic and spectra of fractals has been a subject of significant interest in contemporary mathematics. This book contributes to the literature on the subject in several different and new ways. In particular, the authors provide a rigorous and detailed study of the spectral operator, a map that sends the geometry of fractal strings onto their spectrum. To that effect, they use and develop methods from fractal geometry, functional analysis, complex analysis, operator theory, partial differential equations, analytic number theory and mathematical physics.Originally, M L Lapidus and M van Frankenhuijsen 'heuristically' introduced the spectral operator in their development of the theory of fractal strings and their complex dimensions, specifically in their reinterpretation of the earlier work of M L Lapidus and H Maier on inverse spectral problems for fractal strings and the Riemann hypothesis.One of the main themes of the book is to provide a rigorous framework within which the corresponding question 'Can one hear the shape of a fractal string?' or, equivalently, 'Can one obtain information about the geometry of a fractal string, given its spectrum?' can be further reformulated in terms of the invertibility or the quasi-invertibility of the spectral operator.The infinitesimal shift of the real line is first precisely defined as a differentiation operator on a family of suitably weighted Hilbert spaces of functions on the real line and indexed by a dimensional parameter c. Then, the spectral operator is defined via the functional calculus as a function of the infinitesimal shift. In this manner, it is viewed as a natural 'quantum' analog of the Riemann zeta function. More precisely, within this framework, the spectral operator is defined as the composite map of the Riemann zeta function with the infinitesimal shift, viewed as an unbounded normal operator acting on the above Hilbert space.It is shown that the quasi-invertibility of the spectral operator is intimately connected to the existence of critical zeros of the Riemann zeta function, leading to a new spectral and operator-theoretic reformulation of the Riemann hypothesis. Accordingly, the spectral operator is quasi-invertible for all values of the dimensional parameter c in the critical interval (0,1) (other than in the midfractal case when c =1/2) if and only if the Riemann hypothesis (RH) is true. A related, but seemingly quite different, reformulation of RH, due to the second author and referred to as an 'asymmetric criterion for RH', is also discussed in some detail: namely, the spectral operator is invertible for all values of c in the left-critical interval (0,1/2) if and only if RH is true.These spectral reformulations of RH also led to the discovery of several 'mathematical phase transitions' in this context, for the shape of the spectrum, the invertibility, the boundedness or the unboundedness of the spectral operator, and occurring either in the midfractal case or in the most fractal case when the underlying fractal dimension is equal to ½ or 1, respectively. In particular, the midfractal dimension c=1/2 is playing the role of a critical parameter in quantum statistical physics and the theory of phase transitions and critical phenomena.Furthermore, the authors provide a 'quantum analog' of Voronin's classical theorem about the universality of the Riemann zeta function. Moreover, they obtain and study quantized counterparts of the Dirichlet series and of the Euler product for the Riemann zeta function, which are shown to converge (in a suitable sense) even inside the critical strip.For pedagogical reasons, most of the book is devoted to the study of the quantized Riemann zeta function. However, the results obtained in this monograph are expected to lead to a quantization of most classic arithmetic zeta functions, hence, further 'naturally quantizing' various aspects of analytic number theory and arithmetic geometry.The book should be accessible to experts and non-experts alike, including mathematics and physics graduate students and postdoctoral researchers, interested in fractal geometry, number theory, operator theory and functional analysis, differential equations, complex analysis, spectral theory, as well as mathematical and theoretical physics. Whenever necessary, suitable background about the different subjects involved is provided and the new work is placed in its proper historical context. Several appendices supplementing the main text are also included.
Book Synopsis Operator Algebras and Their Applications by : Robert S. Doran
Download or read book Operator Algebras and Their Applications written by Robert S. Doran and published by American Mathematical Soc.. This book was released on 2016-07-28 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: his volume contains the proceedings of the AMS Special Session Operator Algebras and Their Applications: A Tribute to Richard V. Kadison, held from January 10–11, 2015, in San Antonio, Texas. Richard V. Kadison has been a towering figure in the study of operator algebras for more than 65 years. His research and leadership in the field have been fundamental in the development of the subject, and his influence continues to be felt though his work and the work of his many students, collaborators, and mentees. Among the topics addressed in this volume are the Kadison-Kaplanksy conjecture, classification of C∗-algebras, connections between operator spaces and parabolic induction, spectral flow, C∗-algebra actions, von Neumann algebras, and applications to mathematical physics.
Book Synopsis Completing the Riesz-Dunford Functional Calculus by : John B. Conway
Download or read book Completing the Riesz-Dunford Functional Calculus written by John B. Conway and published by American Mathematical Soc.. This book was released on 1989 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Interpolation Theory and Applications by : Michael Cwikel
Download or read book Interpolation Theory and Applications written by Michael Cwikel and published by American Mathematical Soc.. This book was released on 2007 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the Proceedings of the Conference on Interpolation Theory and Applications in honor of Professor Michael Cwikel (Miami, FL, 2006). The central topic of this book is interpolation theory in its broadest sense, with special attention to its applications to analysis. The articles include applications to classical analysis, harmonic analysis, partial differential equations, function spaces, image processing, geometry of Banach spaces, and more. This volume emphasizes remarkable connections between several branches of pure and applied analysis. Graduate students and researchers in analysis will find it very useful.
Book Synopsis Spectral Theory on the S-Spectrum for Quaternionic Operators by : Fabrizio Colombo
Download or read book Spectral Theory on the S-Spectrum for Quaternionic Operators written by Fabrizio Colombo and published by Springer. This book was released on 2019-01-04 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this monograph is the quaternionic spectral theory based on the notion of S-spectrum. With the purpose of giving a systematic and self-contained treatment of this theory that has been developed in the last decade, the book features topics like the S-functional calculus, the F-functional calculus, the quaternionic spectral theorem, spectral integration and spectral operators in the quaternionic setting. These topics are based on the notion of S-spectrum of a quaternionic linear operator. Further developments of this theory lead to applications in fractional diffusion and evolution problems that will be covered in a separate monograph.
Book Synopsis Noncommutative Geometry by : Alain Connes
Download or read book Noncommutative Geometry written by Alain Connes and published by Springer Science & Business Media. This book was released on 2003-12-08 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
